Question 143266
1.  Use the two-point form of the equation of a straight line to write the equations for the lines containing segments AB and CD.  Then solve each of the equations for y (that is, put them in {{{y=mx+b}}} form)  If the slopes are equal, then the lines are parallel.  If the slopes are negative reciprocals, i.e. {{{m[1]=-1/m[2]}}}, then they are perpendicular.  Otherwise neither.


2.  Apply the midpoint formulas to the coordinates for A and B.  Repeat for the coordinates for C and D.  If you get the same set of coordinates, meaning the midpoint of AB is the same point as the midpoint of CD, then the two segments bisect each other, otherwise not.


3.  Apply the distance formula to the coordinates for A and B.  Do it again for the coordinates for C and D.  If you get the same answer both times, the segments are congruent. Otherwise not.